A data set includes data from student evaluations of courses. The summary statistics are n=97, x=3.66, s=0.63. Use a 0.01 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

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A data set includes data from student evaluations of courses. The summary statistics are n= 97, x= 3.66, s= 0.63. Use a 0.01 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. Assume that a simple
random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
О в. Но: и33.75
O A. Ho: H#3.75
Η: μ= 3.75
OC. Ho: H= 3.75
H1: µ<3.75
H: µ>3.75
O D. Ho: H=3.75
H: u23.75
Determine the test statistic.
(Round to two decimal places as needed.)
Determine the P-value.
(Round to three decimal places as needed.)
State the final conclusion that addresses the original claim.
v Ho. There is
v evidence to conclude that the mean of the population of student course evaluations is equal to 3.75
v correct.
Transcribed Image Text:A data set includes data from student evaluations of courses. The summary statistics are n= 97, x= 3.66, s= 0.63. Use a 0.01 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses? О в. Но: и33.75 O A. Ho: H#3.75 Η: μ= 3.75 OC. Ho: H= 3.75 H1: µ<3.75 H: µ>3.75 O D. Ho: H=3.75 H: u23.75 Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. v Ho. There is v evidence to conclude that the mean of the population of student course evaluations is equal to 3.75 v correct.
Expert Solution
Step 1

Given : n=97 , X-bar=3.66  , s=0.63 , μ0=3.75 , α=0.01

Since , the population standard deviation (σ) is unknown.

Therefore , use t-distribution.

The degrees of freedom is given by,

df=n-1=97-1=96

Our aim is to test the claim that the population of student course evaluation has a mean equal to 3.75

Here , we use one sample mean t-test.

 

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